{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enunciado\n",
    "\n",
    "Crea una función que calcule el punto de encuentro de dos objetos en movimiento\n",
    "en dos dimensiones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cada objeto está compuesto por una coordenada xy y una velocidad de desplazamiento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Objeto:\n",
    "\n",
    "  def __init__(self, x_coor, y_coor, velocity):\n",
    "    \"\"\"\n",
    "    x_coor: coordenada x inicial\n",
    "    y_coor: coordenada y inicial\n",
    "    velocity: velocidad del objeto para 1 unidad de tiempo ([vx, vy])\n",
    "    \"\"\"\n",
    "    self.x = x_coor\n",
    "    self.y = y_coor\n",
    "    self.v = velocity\n",
    "    self.steps = [[self.x, self.y]]\n",
    "\n",
    "  def mover(self, delta_t):\n",
    "    for i in range(delta_t):\n",
    "      self.steps.append([self.x + self.v[0] * i, self.y  + self.v[1] * i])\n",
    "\n",
    "  def mostrar_trayectoria(self, title):\n",
    "\n",
    "    _, ax = plt.subplots()\n",
    "    ax.set(xlabel='x', ylabel='y', title=title)\n",
    "    ax.grid()\n",
    "    ax.plot([x[0] for x in self.steps], [x[1] for x in self.steps])\n",
    "\n",
    "    if self.v[0] > 0:\n",
    "      ax.plot([x[0] for x in self.steps], [x[1] for x in self.steps], '<r')\n",
    "    else:\n",
    "      ax.plot([x[0] for x in self.steps], [x[1] for x in self.steps], '>r')\n",
    "\n",
    "    # Añadimos texto al punto de origen (🌟)\n",
    "    delta_x = 0.1 * self.v[0]\n",
    "    delta_y = 0.1 * self.v[1]\n",
    "    x_pos = self.x + delta_x\n",
    "    y_pos = self.y + delta_y\n",
    "    ax.text(x_pos, y_pos, '٭', fontsize=25, color='green')\n",
    "    # plt.show()\n",
    "\n",
    "  def limpiar_pasos(self):\n",
    "    self.steps = [[self.x, self.y]]\n",
    "\n",
    "  def calcular_ecuacion(self):\n",
    "    m = self.v[1] / self.v[0]\n",
    "    b = self.y - m * self.x\n",
    "    return m, b\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algunos ejemplos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-1.0, 5.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = 0\n",
    "y1 = 5\n",
    "v1 = [1, -1]\n",
    "obj = Objeto(x1, y1, v1)\n",
    "obj.mover(10)\n",
    "\n",
    "title=\"Trayectoria primer objeto después de 10 unidades de tiempo\"\n",
    "obj.mostrar_trayectoria(title=title)\n",
    "print(obj.calcular_ecuacion());\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.0, 0.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x2 = 0\n",
    "y2 = 0\n",
    "v2 = [1, 1]\n",
    "\n",
    "obj2 = Objeto(x2, y2, v2)\n",
    "obj2.mover(10)\n",
    "title=\"Trayectoria segundo objeto después de 10 unidades de tiempo\"\n",
    "obj2.mostrar_trayectoria(title=title)\n",
    "print(obj2.calcular_ecuacion());\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En una sola gráfica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set(xlabel='x', ylabel='y', title=\"Trayectoria de los dos objetos\")\n",
    "ax.grid()\n",
    "ax.plot([x[0] for x in obj.steps], [x[1] for x in obj.steps], label=\"Objeto 1\")\n",
    "if obj.v[0] > 0:\n",
    "  ax.plot([x[0] for x in obj.steps], [x[1] for x in obj.steps], '<r')\n",
    "else:\n",
    "  ax.plot([x[0] for x in obj.steps], [x[1] for x in obj.steps], '>r')\n",
    "ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], label=\"Objeto 2\")\n",
    "if obj2.v[0] > 0:\n",
    "  ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], '<b')\n",
    "else:\n",
    "  ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], '>b')\n",
    "ax.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos con la función:\n",
    "\n",
    "- La función recibirá las coordenadas de inicio de ambos objetos y sus velocidades."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcular_punto_encuentro(x1, y1, v1, x2, y2, v2):\n",
    "\n",
    "  # Creamos los objetos\n",
    "  obj1 = Objeto(x1, y1, v1)\n",
    "  obj2 = Objeto(x2, y2, v2)\n",
    "\n",
    "  # Obtenemos las ecuaciones de las rectas\n",
    "  m1, b1 = obj1.calcular_ecuacion()\n",
    "  m2, b2 = obj2.calcular_ecuacion()\n",
    "\n",
    "  # print('m1:', m1, 'b1:', b1)\n",
    "  # print('m2:', m2, 'b2:', b2)\n",
    "\n",
    "  print(f'y1 = {m1} * x1 + {b1}')\n",
    "  print(f'y2 = {m2} * x2 + {b2}')\n",
    "\n",
    "  # Calculamos el punto de encuentro\n",
    "\n",
    "  # Si las pendientes son iguales, o son la misma recta\n",
    "  # (siempre se encuentran) o nunca se encuentran\n",
    "  if m1 == m2:\n",
    "    if b1 == b2:\n",
    "      print(\"Las rectas son la misma!\")\n",
    "    else:\n",
    "      print(\"Las rectas nunca se encuentran (son paralelas)\")\n",
    "    return\n",
    "\n",
    "  # (Resolvemos el sistema de ecuaciones)\n",
    "  x = (b2 - b1) / (m1 - m2)\n",
    "  y = m1 * x + b1\n",
    "\n",
    "  # Mostramos el resultado\n",
    "  # print(f\"Posible punto de encuentro en: ({x}, {y})\")\n",
    "\n",
    "  # Calculamos el tiempo de encuentro para cada objeto\n",
    "  # para comprobar que hay una colisión\n",
    "  t1 = (x - x1) / v1[0]\n",
    "  t2 = (x - x2) / v2[0]\n",
    "\n",
    "  # Función auxiliar para graficar los objetos\n",
    "  def graficar_trayectoria():\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set(xlabel='x', ylabel='y', title=f'Colisión en ({x}, {y})')\n",
    "    ax.grid()\n",
    "    ax.plot([x[0] for x in obj1.steps], [x[1] for x in obj1.steps], label=\"Objeto 1\")\n",
    "    if obj1.v[0] > 0:\n",
    "      ax.plot([x[0] for x in obj1.steps], [x[1] for x in obj1.steps], '<r')\n",
    "    else:\n",
    "      ax.plot([x[0] for x in obj1.steps], [x[1] for x in obj1.steps], '>r')\n",
    "    ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], label=\"Objeto 2\")\n",
    "    if obj2.v[0] > 0:\n",
    "      ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], '<b')\n",
    "    else:\n",
    "      ax.plot([x[0] for x in obj2.steps], [x[1] for x in obj2.steps], '>b')\n",
    "    # Colocamos el punto de encuentro\n",
    "    ax.plot(x, y, 'go', label=\"Punto de encuentro\")\n",
    "    ax.text(x, y, '¶', fontsize=25, color='green')\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "\n",
    "  # Si los tiempos son iguales, hay colisión\n",
    "  if t1 == t2:\n",
    "    if t1:\n",
    "      print(f\"Tiempo de encuentro: {t1}\")\n",
    "    else:\n",
    "      print(\"Hay colisión en el punto de origen\")\n",
    "    # Mostramos la trayectoria de los objetos\n",
    "    obj1.mover(math.ceil(t1) + 1)\n",
    "    obj2.mover(math.ceil(t2) + 1)\n",
    "    graficar_trayectoria()\n",
    "\n",
    "  else:\n",
    "    # print(f't1: {t1}, t2: {t2}')\n",
    "    print(\"No hay colisión\")\n",
    "\n",
    "  # print(f\"El tiempo de encuentro es: {distancia}\")\n",
    "\n",
    "  return\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo #1 (colisión)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y1 = -1.0 * x1 + 6.0\n",
      "y2 = 1.0 * x2 + 0.0\n",
      "Tiempo de encuentro: 3.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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ylRUVFZWElKZNm17x9oqLi8nPz8fZ2Vlfvpegvqqay+2vRo0aAZCeno6Pj88VDQPppyQicpWdvybFxcXF5EpEas754/tKr8FSUBERMYmukZD6rLqObwWVyiouhuxss6sQERFpUEwPKklJSfzxj3+kadOmuLi40LVrV6Kjo80uq1RxMbzyCri7Q+PGsHGj2RWJiNR6LVq04K233rridURMDSonTpzg2muvxcHBgaVLlxIbG8ubb76Jl5eXmWXZFBfT9ptvsG/SBJ57DnJzbaHlwAGzKxMRMU1CQgL33XcfAQEBODo6EhISwqRJkzh27FiVt7V582buv//+Sq8/bdo0unbtWuX9VGT69On06dMHFxeX2vGdIxdk6qyf1157jeDgYGbPnl3S1qJFC/MKAigupnj6DKzTX6HjmTMY5lYjIlJrHDp0iN69e9OuXTu+/PJLWrZsye7du3nyySdZunQpGzZsoEmTJpXeXrNmzWqw2ovLz89n3Lhx9O7dm48++si0OuTSTA0q3377LUOHDmXcuHGsXbuWwMBAHnjgAf785z9XuH5eXh55eXklr7PPXTNSUFBwxVcVA1jfeAPryy9jzc0tCSi/vxSooKgIqmFf9cn5vq+On0F9p76qvPrcVwUFBRiGQXFxMcXFxVe8PcMwSv5bHdu7kAceeABHR0eWLVtWMv00KCiI8PBw2rZty+TJk5k5c2bJ+tnZ2dx+++189913eHh48Mwzz/DQQw+VLG/VqhWTJk1i0qRJAGRlZfHUU0+xaNEizp49S/fu3XnzzTcJDw9nzpw5vPDCC0DpRZofffQRd999N/Hx8fz973/nxx9/xGq1MnToUN555x18fX3LfYbzfTV16lQsFgtz5swBqNF+q8uu5NgqLi7GMAwKCgrKTU+uyt9rU4PKoUOHmDVrFo899hiTJ09m06ZN/P3vf8fJyYmJEyeWW3/GjBklB+pvrVixolqm+d30j39gKSwEygeU8zZHbyPD0/OK91UfrVy50uwS6gz1VeXVx76yt7fHz8+PU6dOkZ+fD9i+CM4WXNmX5ZljJ6v8HmcHa6VmZ5w4cYIVK1bw3HPPlfvHoYuLC+PGjWPu3LnMmDEDi8VCcXExb7zxBo8++ihr1qzhxx9/5LHHHiM4OJgBAwYAti+ys2fPkp2djWEYDB8+nMaNGzN37lw8PDyYM2cOgwYNYsuWLQwfPpyHHnqIVatWsXDhQgA8PDzIyspi1KhRuLi48P3331NYWMgTTzzBuHHj+P777y/4eXJycgA4e/YshmGU/MNXKna+v6oiPz+fM2fOsG7dOgrPfbeel5ubW+ntmBpUiouL6d69O9OnTwegW7du7N69m1mzZlUYVJ599lkee+yxktfZ2dkEBwczZMgQPDw8rrygF1/EePllLOfOqFT0V3feEXvycoK4pZs/17Zuir2d6dcjm66goICVK1cyePBgHBwczC6nVlNfVV597quzZ8+SkJCAm5sbzs7OAOTmF9LttasfynZNG4yL46W/CuLi4jAMg65du1b4+zYsLIxPPvmEvLw8fHx8sFqt9OnTh6lTpwIQERFBdHQ0H3zwAaNGjQLAarXi7OyMh4cHP/74I3FxcaSmpuLk5ATYvhOWLl3K8uXLuf/++2nSpAlOTk60bdu2ZL8rV65k9+7dHDx4kODgYAA+++wzunTpwt69e+nRo0eZOg3DICcnB3d3dywWC87Ozlgslur5DqmHft9fVXH27FkaNWpE3759S47z86oSDE0NKv7+/nTs2LFMW2hoKFFRURWu7+TkVHIA/5aDg0P1/CJ79ll4+mmYMQOmT4cKAkthcTGLd6WyeFcqzdyduLVbIGMig2jn637l+6/jqu3n0ACoryqvPvZVUVERFosFq9VacrdPs+6S+tsaLrVeZda3s7MrWd6nT58y6/bp04e33nqrTNv5fti6dSunTp0qd93KmTNnOHz4MFZr6Zmf375/7969BAcHExISUtLWuXNnvLy82Lt3L7169SqzvfPDF7Wl/2u73/dXVZz/mVX0d7gqf6dNDSrXXnste/fuLdO2b9++MgfcVWe1wpQpFD7xBPvvu4/QBQtsM37OeXJoe5o0b8GibUlk5OTx/rpDvL/uEF0CPRkbGcTN4QE0dnU0r34RqZMaOdgR++LQy3pvcXExOdk5uHu4V/nLpJFD5W5t3qZNGywWC7GxsYwePbrc8j179tC4cWO8vb0vup0L/au8uLgYf39/1qxZU27ZxWblGIZR4TYv1C51j6lB5dFHH6VPnz5Mnz6d8ePHs2nTJj744AM++OADM8uysVrZP24cbT/6CIc33rCdYTl7luBeXZnWoxOTR4Syem8686ITWb0nnZ1JWexMyuLlxbEM7ODLmMgg+rdvhoOGhkSkEiwWS6WGYCpSXFxMoaMdLo72NXZmoGnTpgwePJiZM2fy6KOPllxMC7YHLH7++edMnDixTDjYsGFDmW1s2LCBDh06VLj9iIgIUlNTsbe3v+DsT0dHR4qKisq0dezYkfj4eBISEkqGfmJjY8nKyiI0NPRyPqrUMqZ+i/bo0YMFCxbw5Zdf0rlzZ1566SXeeust7rjjDjPLKuvcGRZycuDECTg33ulob2VoJz/+b2J3Nk4eyNSRHekU4EFBkcGy3an8+X9buGb6D7z4XSy7k7NM/hAiIlfu3XffJS8vj6FDh7Ju3ToSEhJYtmwZgwcPJjAwkFdeeaXM+r/88guvv/46+/bt47333uObb74pmeHze4MGDaJ3796MHj2a5cuXc+TIEdavX89zzz3Hli1bANvtKw4fPsy2bdvIzMwkLy+PQYMGERYWxh133EFMTAybNm1i4sSJ9OvXj+7du1/ws8THx7Nt2zbi4+MpKipi27ZtbNu2jVOnTlVfh0m1MP3pyTfddBM33XST2WVcmtUKF7jYqqmbE/dc25J7rm1JXEo2UdGJLNyWTOapPD7+5TAf/3KYUH8PxkQEMrpbIN5u5a+zERGp7dq2bcuWLVuYNm0at912G8eOHcPPz4/Ro0czderUcvdQefzxx4mOjuaFF17A3d2dN998k6FDKx7eslgsLFmyhClTpnDvvfeSkZGBn58fffv2LZlmPGbMGObPn8+AAQM4efIks2fP5u6772bhwoU8/PDD9O3bF6vVyrBhw/jPf/5z0c8ydepU/ve//5W87tatGwCrV6+mf//+V9BLUt1MDyr1Tai/B8/d1JFnhndg3f4M5kUnsio2nbiUbF5enM2MpXsY0L4ZYyKCuCHUByf7y3/0tYjI1RYSElLmJp0XcuTIkUuuk5eXh5ubW8lrd3d33nnnHd55550K13dycmLevHnl2ps3b86iRYsuub/fmj17Np988kmV3iPmUFCpIfZ2Vm7o4MsNHXw5mZvPdztSmBedyPaEk6yKS2dVXDpeLg7cHB7AmIggwoI8deGXiDQIubm5/PLLL6SlpdGpUyezy5FaTkHlKvByceTOa0K485oQDqTnEBWTxPyYRNKy8/jfr0f5369HaePjxtjIIG7pFoivh/OlNyoiUkd98MEHvPTSSzzyyCP07t3b7HKkllNQucra+Ljz9LAOPDGkPb8cyGRedCLLd6dyIP0Ury7dw+vL9nB922aMiQxiSEdfnCs5dVBEpK545JFHeOSRR8wuQ+oIBRWT2Fkt9G3XjL7tmpF9toAl54aGthw9wdp9Gazdl4G7sz03hQUwNjKQiOaNNTQkIiINjoJKLeDh7MAfejbnDz2bczjzNPNjEpkfk0TSyTN8uSmeLzfF09LblTERgdwSEUSgV6NLb1RERKQeUFCpZVp6u/L4kPY8OqgdGw4fY150Ikt3pnI48zRvrNjHmyv30ad1U8ZEBDGss99l3yBKRESkLtC3XC1ltVro09qbPq29eXFUIUt3phAVk8iGQ8f55cAxfjlwjOcX7mJEF3/GRAbRs0UTrFYNDYmISP2ioFIHuDnZM657MOO6B5NwPJf5MUlExSQSfzyXb6IT+SY6keAmjbi1WxBjIoJo3tTF7JJFRESqhYJKHRPcxIVJg9ry94Ft2HzkBFHRiSzemULC8TO8/cN+3v5hPz1bNmFsRBAjwvxxc9KPWERE6i49Ma+Oslgs9GzZhNfGhrF5yiDeuq0r17f1xmKBTYeP81TUDnq8vIpH527j5/2ZFBUbZpcsIg1IixYteOutt654HREFlXqgkaMdo7sF8ul9vVj/zA08ObQ9rZq5cqagiAVbk/jjRxu5/rUf+efyPRzK0AO3ROTyJSQkcN999xEQEICjoyMhISFMmjSJY8eOVXlbmzdv5v7776/0+tOmTaNr165V3s/vxcfH86c//YmWLVvSqFEjWrduzdSpU8nPz7/ibUv107hAPePv2YgHB7Thgf6t2ZZwknnRiXy3PZnkrLO8t/og760+SERzL8ZEBnFTWACejRzMLllE6ohDhw7Ru3dv2rVrx5dffknLli3ZvXs3Tz75JEuXLmXDhg3lHkx4Mc2aNavBai9s3759FBcX8/7779OmTRt27drFn//8Z06fPs0bb7xhSk1yYTqjUk9ZLBa6NW/MK7d0YdOUQbw7oRsD2jfDaoGY+JNMWbCLHq+s4qEvYli9N53ComKzSxaRWu7BBx/E0dGRFStW0K9fP5o3b87w4cNZtWoVSUlJTJkypcz6OTk5TJgwATc3NwICAso90fj3Qz9ZWVncf//9+Pj44OHhwQ033MD27dsBmDNnDi+88ALbt2/HYrFgsViYM2cOYDtDMmrUKNzc3PDw8GD8+PGkpaVd8HMMGjSIjz/+mCFDhtCqVStuvvlmnnjiCebPn189HSXVSmdUGgBnBztuCgvgprAA0rPPsnBbElHRSexNy+H7HSl8vyMFH3cnbukWyJjIINr5uptdskjDYxhQkHt57y0utr033w6sVfz3p4MLVOKu18ePH2f58uW88sorNGpU9qaTfn5+3HHHHcydO5eZM2eW3EX7n//8J5MnT2batGksX76cRx99lA4dOjB48OBy2zcMgxtvvJEmTZqwZMkSPD09ef/99xk4cCD79u3jtttuY9euXSxbtoxVq1YB4OnpiWEYjB49GldXV9auXUthYSEPPPAAt912G2vWrKl0N2RlZVXpbJBcPQoqDYyPhzP3923Nn69vxe7kbOZFJ7JoWxLpOXm8v+4Q7687RFiQJ2Migrg5PIDGro5mlyzSMBTkwvSAy3qrFfC63P1OTgZH10uutn//fgzDIDQ0tMLloaGhnDhxgoyMDHx8fAC49tpreeaZZwBo164dv/zyC//+978rDCqrV69m586dpKen4+TkBMAbb7zBwoULmTdvHvfffz9ubm7Y29vj5+dX8r6VK1eyY8cODh8+THBwMACffvopnTp1YvPmzfTo0eOSn+3gwYP85z//4c0337zkunL1Kag0UBaLhc6BnnQO9GTyiFB+3JNOVEwiq/eksyMxix2JWby8OJaBHXwZExlE//bNcLDTSKGIVMwwbDMLf/tMst8/Gbl3794XnOUTHR3NqVOnaNq0aZn2M2fOcPDgwQvuNy4ujuDg4JKQAtCxY0e8vLyIi4u7ZFBJTk5m2LBhjBs3jj/96U8XXVfMoaAiONpbGdbZj2Gd/Th2Ko9F25KJiklkd3I2y3ansmx3Kk1dHRnVNZCxkUF0DPAwu2SR+sfBxXZ24zIUFxeTnZODh7s71ssZ+qmENm3aYLFYiI2NZfTo0eWW79mzh8aNG+Pt7X3R7Vzo4arFxcX4+/tXOFzj5eV1we0ZhlHhNi/U/lvJyckMGDCA3r1788EHH1x0XTGPgoqU0dTNiXuva8m917UkLiWbqOhEFm5LIvNUPh//cpiPfzlMqL8HYyICGd0tEG83J7NLFqkfLJZKDcFUqLgYHIps769qUKmkpk2bMnjwYGbOnMmjjz5a5jqV1NRUPv/8cyZOnFgmHGzYsKHMNjZs2ECHDh0q3H5ERASpqanY29vTokWLCtdxdHSkqKioTFvHjh2Jj48nISGh5KxKbGwsWVlZFxymAkhKSmLgwIFERkYye/bsqgc8uWr0k5ELCvX34LmbOvLrswP56K7ujOjih6OdlbiUbF5eHMc103/gT59sZvnuNAo1aUik3nv33XfJy8tj6NChrFu3joSEBJYtW8bgwYMJDAzklVdeKbP+L7/8wuuvv86+fft47733+Oabb5g0aVKF2x40aBC9e/dm9OjRLF++nCNHjrB+/Xqee+45tmzZAthmCR0+fJht27aRmZlJXl4egwYNIiwsjDvuuIOYmBg2bdrExIkT6devH927d69wXykpKdxwww0EBwfzxhtvkJGRQWpqKqmpqdXbYVItdEZFLsnBzsrAUF8GhvpyMjef77YnMy8mie0JJ1kVl86quHRc7O3YShzjezSnS6DnJU+5ikjd07ZtW7Zs2cK0adO47bbbOHbsGH5+fowePZqpU6eWmzXz+OOPEx0dzQsvvIC7uztvvvkmQ4cOrXDbFouFJUuWMGXKFO69914yMjLw8/Ojb9+++Pr6AjBmzBjmz5/PgAEDOHnyJLNnz+buu+9m4cKFPPzww/Tt2xer1cqwYcPKTYX+rdWrV3PgwAEOHDhAUFBQmWXnr7WR2kNBRarEy8WRO3u34M7eLTiQnsO86CQWxCSSlpPHZxsT+GxjAm193BgTGcQt3QLx9XA2u2QRqUYhISHMnj37kusdOXLkkuvk5eXh5uZW8trd3Z133nmHd955p8L1nZycmDdvXrn25s2bs2jRokvu77wJEybw17/+VcM9dYR+SnLZ2vi488zwDqx9oi9/DS3ipi5+ONlb2Z9+ileX7qH3jB+46+NNfLs9mbMFRZfeoIg0CLm5uaxcuZK0tDQ6depkdjlSy+mMilwxO6uFUC+Dx0eEcaYIFu9IISo6kS1HT7B2XwZr92Xg7mzPTWEBjI0MIqK5l4aGRBqwDz74gJdeeolHHnmk3BRmkd9TUJFq5eHswO09m3N7z+YczjzN/JhE5sckkXTyDF9uiufLTfG09HZlTEQgt0QEEejV6NIbFZF65ZFHHuGRRx4xuwypIxRUpMa09Hbl8SHteXRQOzYcOsa8mESW7kzlcOZp3lixjzdX7qNP66aMjQxiaCc/XBx1OIqISFn6ZpAaZ7Va6NPGmz5tvHlxVCFLd6YQFZPIhkPH+eXAMX45cAxXx12M6OLP2MggerRogtWqoSEREVFQkavMzcmecd2DGdc9mITjucyPSSIqJpH447l8E53IN9GJBDdpxJiIIMZEBBHcpHJ3zRQRkfpJQUVME9zEhUmD2vL3gW3YfOQEUdGJLN6ZQsLxM7y1aj9vrdpPz5ZNGBsZxIgu/rg56XAVEWlo9JtfTGexWOjZsgk9WzZh2s2dWL47laiYRH4+kMmmw8fZdPg4UxftZlhnP8ZGBtG7VVMNDYmINBAKKlKrNHK0Y3Q323OEkk+eYcHWJKKiEzmUeZoFW5NYsDWJAE9nbo0IYkxkEC29L/PZKCIiUicoqEitFeDViAcHtOGB/q3ZmnCSqOhEvtueTHLWWd5dfYB3Vx8gorkXYyODuTHMH89GDmaXLCK13D333ENmZibfffed2aVIJenOtFLrWSwWIpo35pVburBpyiDendCNAe2bYbVATPxJJi/YSY9XVvHQFzGs2ZtOUbGe1SENQ1FxEWuOrOHLXV/yc+LPFBXX7B2g7777biwWCxaLBQcHB1q1asUTTzzB6dOnq3U/FouFhQsXVus2pWJ1oa91RkXqFGcHO24KC+CmsADSs8+ycFsS86IT2Zd2iu93pPD9jhR83J24pVsgYyKDaOfrbnbJIjViftx8Ji2bRGJ2YklbkHsQbw9/m1tDb62x/Q4bNozZs2dTUFDATz/9xJ/+9CdOnz7NrFmzamyfYq6CggJT968zKlJn+Xg4c3/f1ix/pC/fPXQdd/dpQWMXB9Jz8nh/3SGG/HsdN7/7M//79QgnTuebXa5ItZkfN5+xX48tE1IAknKSGPv1WObHza+xfTs5OeHn50dwcDATJkzgjjvuKPkX+d13383o0aPLrP/II4/Qv3//ktf9+/fn73//O0899RRNmjTBz8+PadOmlSxv0aIFALfccgsWi6XkNcCsWbNo3bo1jo6OtG/fnk8//fSitRYVFfHYY4/h5eVF06ZNeeqpp8o9HdkwDF5//XVatWpFo0aNCA8Pr/DBh7+Vn5/PU089RWBgIK6urvTq1Ys1a9aULJ8zZw5eXl4sX76c0NBQ3NzcGDZsGCkpKWW28/HHH9OpUyecnJzw9/fnoYceAmwPdLRYLGzbtq1k3ZMnT2KxWMrsJzY2lhEjRuDm5oavry933nknmZmZJcsvt6+nTZtG165d+fjjj2nTpg2+vr4YhkF8fDyjRo3Czc0NDw8Pxo8fT1pa2kX7qjooqEidZ7FY6BLkybSbO7Fx8iD++8dIBnf0xd5qYUdiFv9YtJue01fx10+jWRWbRkFRsdkli1y2ouIiJi2bhEH5Ic7zbY8se6TGh4HOa9SoUZX/xf3JJ5/g6urKxo0bef3113nxxRdZuXIlAJs3bwZg9uzZpKSklLxesGABkyZN4vHHH2fXrl385S9/4Z577mH16tUX3M+bb77Jxx9/zEcffcTPP//M8ePHyw1zPPfcc8yePZtZs2axe/duHn30Uf74xz+ydu3aC273nnvu4ZdffuGrr75ix44djBs3jmHDhrF///6SdXJzc3njjTf49NNPWbduHfHx8TzxxBMly2fNmsWDDz7I/fffz86dO/n2229p06ZNpfswJSWFfv360bVrV7Zs2cKyZctIS0tj/PjxZda7nL4GOHDgAF9//TXffPMN69atA2D06NEcP36ctWvXsnLlSg4ePMhtt91W6Zovm1GHZWVlGYCRlZVV7dvOz883Fi5caOTn51f7tuub2tpXGTlnjY9+OmQMf2udEfL09yV/Il9aYbz43W5jd1L1HzeXUlv7qjaqz3115swZIzY21jhz5kyV37v68GqDaVzyz+rDq6u97rvuussYNWpUyeuNGzcaTZs2NcaPH1/hcsMwjEmTJhn9+vUred2vXz/juuuuK7NOjx49jKeffrrkNWAsWLCgzDp9+vQx/vznP5dpGzdunDFixIgL1uvv72+8+uqrJa8LCgqMoKAgY8SIEUZRUZFx6tQpw9nZ2Vi/fn2Z9913333G7bffXuE2Dxw4YFgsFiMpKalM+8CBA41nn33WMAzDmD17tgEYBw4cKFn+3nvvGb6+viWvAwICjClTplS4j8OHDxuAsXXr1pK2EydOGICxevVqwzAM4/nnnzeGDBlS5n0JCQkGYOzdu9cwjMvv66lTpxoODg5Genq6UVRUZJw4ccJYtmyZYWdnZ8THx5est3v3bgMwNm3aVOHnuNhxXpXvb12jIvWWt5sT917Xknuva0lcSjZR0Yks3JZE5ql8Pvr5MB/9fJhQfw/GRgYxqmsA3m5OZpcsckkpOSmXXqkK61XV999/j5ubG4WFhRQUFDBq1Cj+85//VGkbYWFhZV77+/uTnp5+0ffExcVx//33l2m79tprefvttytcPysri5SUlDJPZ7a3tycyMrLkDFBsbCxnz55l8ODBZd6bn59Pt27dKtxuTEwMhmHQrl27Mu15eXk0bdq05LWLiwutW7eu8DOmp6eTnJzMwIEDL/qZLyY6OprVq1fj5uZWbtnBgwdL6rucvgYICQmhWbNmFBfbzkDv2bOH4OBggoODS9bp2LEjXl5exMXF0aNHj8v+LJeioCINQqi/B8/d1JGnh3dg3b4M5kUn8kNcOnEp2bz0fSwzlsTRv70PYyMDuaGDL472GhWV2snf3b9a16uqAQMGMGvWLBwcHAgICMDBofS2AFartdw1IBUNC/32PWAbvj3/hXgxFkvZGz0ahlGurSrO73Px4sUEBgaWWebkVPE/XIqLi7GzsyM6Oho7O7syy34bGir6jOf7plGjiz813mq1/f75bV/+vh+Li4sZOXIkr732Wrn3+/uX/uwvt69dXcveo+pCfX2lP4PKUFCRBsXBzsrAUF8GhvpyMjef77YnMy86ke2JWayKS2NVXBpeLg6MCg9gTGQQXQI9a/wvoUhVXN/8eoI8gkjKTqrwOhULFoI8gri++fU1sn9XV9cLXkvRrFkzdu3aVaZt27Zt5b4sL8XBwYGiorLX2ISGhvLzzz8zceLEkrb169cTGhpa4TY8PT3x9/dnw4YN9O3bF4DCwkJiYmLo0qULYDsj4OTkRHx8PP369atUbd26daOoqIj09HSuv/7y+tjd3Z0WLVrwww8/MGDAgHLLmzVrBtiuQzl/Zue3F9YCREREEBUVRYsWLbC3v/yv8or6uiKhoaHEx8eTkJBQclYlNjaWrKysC/4Mqov+2SgNlpeLI3f2bsGih65j5aN9+Uu/Vvh6OHEyt4BPfj3Kze/+wtC31vH+2oOkZ581u1wRAOysdrw9zDbcYaFsiD7/+q1hb2FntSv33pp2ww03sGXLFv73v/+xf/9+pk6dWi64VMb5L/HU1FROnDgBwJNPPsmcOXP473//y/79+/nXv/7F/Pnzy1yg+nuTJk3i1VdfZcGCBezZs4cHHniAkydPlix3d3fniSee4NFHH+WTTz7h4MGDbN26lffee49PPvmkwm22a9eOO+64g4kTJzJ//nwOHz7M5s2bee2111iyZEmlP+O0adN48803eeedd9i/fz8xMTElQ2iNGjXimmuu4dVXXyU2NpZ169bx3HPPlXn/gw8+yPHjx7n99tvZtGkThw4dYsWKFdx7772VCh7nVdTXFRk0aBBhYWHccccdxMTEsGnTJiZOnEi/fv3o3r17pfd3ORRURIC2vu48OzyU9c8M5JN7ezIyPAAneyv70k4xY+kerpnxA3fP3sR325M5W3B1ZlOIXMitobcyb/w8Aj3KDlcEeQQxb/y8Gr2PysUMHTqU559/nqeeeooePXqQk5NT5gxIZb355pusXLmS4ODgkjMKo0eP5u233+af//wnnTp14v3332f27Nllpj7/3uOPP87EiRO5++676d27N+7u7uWmT7/00kv84x//YMaMGYSGhjJ06FC+++47WrZsecHtzp49m4kTJ/L444/Tvn17br75ZjZu3Fjm+o1Lueuuu3jrrbeYOXMmnTp14qabbioza+jjjz+moKCA7t27M2nSJF5++eUy7w8ICOCXX36hqKiIoUOH0rlzZyZNmoSnp2fJ0FFlVNTXFTl/Y7jGjRvTt29fBg0aRKtWrZg7d26l93W5LMbvBxTrkOzsbDw9PcnKysLDw6Nat11QUMCSJUsYMWJElU9bNjT1ta+yzxaweEcK86ITiT5a+i8Nd2d7RoYHMCYiiIjmXlUaGqqvfVUT6nNfnT17lsOHD9OyZUucnZ0veztFxUX8FP8TSdlJeFo9GdphKA729auvqltxcTHZ2dl4eHhU6Qu9obqS/rrYcV6V729doyJyAR7ODtzeszm392zO4czTzI9JJCo6keSss3yxMZ4vNsbTytuVMZFB3NItkACvi18gJ1Ld7Kx29G/Rv+TLxIzhHpGapqAiUgktvV15fEh7Hh3Ujg2HjjEvOpGlu1I5lHmafy7fyxsr9nJta2/GRAYytJMfLo6V/KtlGJCfDxeYYSAi0tCZet5r2rRpJQ+4Ov/Hz8/PzJJELspqtdCnjTf/uq0rm58bxD/HhtGrZRMMA34+kMmjc7fT4+VVPDVvOxsPHSs3VbOEYcDy5dCrF4SEQELC1f0gIiJ1hOlnVDp16sSqVatKXv9+XrpIbeXmZM+47sGM6x5MwvFc5sckERWTSPzxXL7eksjXWxIJbtKIMRFBjIkIIriJCxgGzbZuxe6llyA6GqxWKC6GjAyowoV4IiINhelBxd7eXmdRpM4LbuLCpEFt+fvANmw+coJ50Qks2ZlKwvEzvLVqP2+t3Mf9Z/bzl1Vz6BO3A+N8IK/EjZek/qrDcxlELqm6jm/Tg8r+/fsJCAjAycmJXr16MX36dFq1alXhunl5eeTl5ZW8zs7OBmyzA6r7MdTnt2f2463rAvVVWd2C3OkW1JHnhrdnRVw6+z5fyI1fvUt46n4KLbbRVsvv7nNQUFgI6r8y6vtxZRgGp06duuAdUKu6rfP/rcxdRxsy9VXVXEl/nTp1quT9v/97XJW/16ZOT166dCm5ubm0a9eOtLQ0Xn75Zfbs2cPu3bvLPDPhvGnTpvHCCy+Ua//iiy9wcXG5GiWLVNmAhx7CIzHxouvMn/4mdh1bX3QdqV/c3d1p3Lgx3t7eODo66g7IUm8YhkF+fj6ZmZmcOHGCnJyccuvk5uYyYcKESk1PrlX3UTl9+jStW7fmqaee4rHHHiu3vKIzKsHBwWRmZtbIfVRWrlzJ4MGD6909HKqb+uriLD/8gPW557BGR2PY2ZU7mwJw411v4dSzO7d0DWBEZ188Gqkf6/txZRgG6enpJWeGr3RbZ8+exdnZWYHnEtRXVXMl/eXh4YGPj0+F78vOzsbb27vu3UfF1dWVLl26lLk73285OTlVeJrUwcGhxn6R1eS26xv11QUMGwZDh8KKFRhTpmCpILBYLRATf5KY+JO8vGQPQzr5MSYikOvbNsPO2rB/mdbn4yooKIiioqIrHt4qKChg3bp19O3bt972VXVRX1XN5faXg4PDRSfHVGVbtSqo5OXlERcXd9kPehKptSwWGDqUogED2DB9Otd8/z2W38z6mXNPT+YZPkTFJLIv7RTfbU/mu+3J+Lg7cUtEIGMjgmjr6272p5AaYGdnd8WzHe3s7CgsLMTZ2Vlfvpegvqqa2tBfpt5H5YknnmDt2rUcPnyYjRs3MnbsWLKzs7nrrrvMLEuk5lgsZHTrRtH69bBsGURGgp8fTVsF85d+rVn+SF++e+g67uodgpeLA+k5eby/9hCD/72OUe/+zP9+PcKJ0/lmfwoRkavG1DMqiYmJ3H777WRmZtKsWTOuueYaNmzYQEhIiJllidS8c2dYGDKkzJ1pLRYLXYI86RLkyZQbO/LjnnTmRSeyZm862xOz2J6YxUvfxzIo1JcxEUH0a98MBzs9r0RE6i9Tg8pXX31l5u5FzGexXPD2+Y72VoZ19mNYZz8yT+WxaFsyUdGJxKZks3RXKkt3peLt5sioroGMiQiiY0D1XlAuIlIb1KprVESkYt5uTtx3XUvuu64lscnZRMUksmhbEpmn8vno58N89PNhOvp7MCYyiFFdA/B207ODRKR+UFARqWM6BnjQMaAjzwzvwNq9GUTFJPJDXDqxKdnEfh/LjCVx9G/vw9jIQG7o4IujvYaGRKTuUlARqaMc7KwM6ujLoI6+nDidz3c7bEND2xOzWBWXxqq4NBq7OHBzeABjI4PpHOih+0aISJ2joCJSDzR2dWRi7xZM7N2C/Wk5zItJZEFMEuk5eXzy61E++fUo7XzdGBMRxC3dAvHxcDa7ZBGRSlFQEaln2vq68+zwUJ4c0p6fD2QSFZPE8t2p7Es7xYyle3ht2R76tmvGmIggBnf0xdlBTywXkdpLQUWknrK3s9K/vQ/92/uQdaaAxTtSiIpJJProCdbszWDN3gw8nO25KTyAMRFBRDT30tCQiNQ6CioiDYBnIwcm9GrOhF7NOZRxivkxScyPSSQ56yxfbIzni43xtPJ2ZUykbWgowKuR2SWLiAAKKiINTqtmbjwxtD2PDW7Hr4eOERWdyNJdqRzKPM0/l+/ljRV7uba1N2MiAxnWyZ9GjhoaEhHzKKiINFBWq4Vr23hzbRtvXhxdyJKdKURFJ7Lx8HF+PpDJzwcyed5pNyO6+DEmIoieLZtoaEhErjoFFRHBzcme8d2DGd89mITjuUTFJBIVk0jC8TN8vSWRr7ck0ryJC7dG2O6CG9zExeySRaSBUFARkTKCm7jwyKB2/P2Gtmw+cpyomEQW70gh/ngub63az1ur9tOrZRPGRAYxoos/bk76NSIiNUe/YUSkQlarhV6tmtKrVVOm3dyJ5btTiYpO4peDmWw8fJyNh48zddFuhnf2Y2xkENe0aorVqqEhEaleCioickkujvbc0i2IW7oFkXzyDAu2JhEVncihzNPM35rE/K1JBHo14pZugYyJDKKlt6vZJYtIPaGgIiJVEuDViAcHtOGB/q2JiT9JVEwi321PJunkGd5dfYB3Vx8gMqQxYyODuDHMHw9nB7NLFpE6TEFFRC6LxWIhMqQxkSGN+cdNHVkZm0ZUTCLr9mUQffQE0UdPMO3b3Qzp5MeYiECub9sMOw0NiUgVKaiIyBVzdrBjZHgAI8MDSMs+y8KtSUTFJLIv7RTfbU/mu+3J+Ho4MbpbIGMjgmjr6252ySJSRyioiEi18vVw5i/9WnN/31bsTMoiKjqRRduTScvO4/21h3h/7SHCgzwZExnEzeEBeLk4ml2yiNRiCioiUiMsFgthQV6EBXkx+cZQVu9JZ150Emv2prM9MYvtiVm8/H0cA0N9GBsZRN92zXCws5pdtojUMgoqIlLjnOztGNbZn2Gd/ck8lceibclERScSm5LN0l2pLN2VirebI6O6BjI2MohQfw+zSxaRWkJBRUSuKm83J+67riX3XdeS2ORsomISWbg1icxT+Xz082E++vkwHf09uKWbPy4FZlcrImZTUBER03QM8KBjQEeeGd6BtXsziIpJZFVcGrEp2cSmZGO12PHjqa2M696cGzr44GivoSGRhkZBRURM52BnZVBHXwZ19OXE6Xy+25HMN1sS2JmUzQ97MvhhTwaNXRy4OTyAsZHBdA700AMSRRoIBRURqVUauzoysXcLbu8eyMfzlpDp3oZF21NIz8njk1+P8smvR2nn68bYyCBGdw3Ex8PZ7JJFpAYpqIhIreXnAvcObcfTw0P5+UAmUTFJLN+dyr60U0xfsodXl+6hb7tmjI0MYlCoL84OdmaXLCLVTEFFRGo9ezsr/dv70L+9D1lnCli8I4WomESij55gzd4M1uzNwMPZnpvCAxgbGUS3YC8NDYnUEwoqIlKneDZyYEKv5kzo1ZxDGaeYH5PE/JhEkrPO8sXGeL7YGE8rb1fGRAZxS7dAArwamV2yiFwBBRURqbNaNXPjiaHteWxwO349dIyo6ESW7krlUOZp/rl8L2+s2Mu1rb0ZGxnE0E5+NHLU0JBIXaOgIiJ1ntVq4do23lzbxpsXRxeyZGcKUdGJbDx8nJ8PZPLzgUzcnOwZ0cWPsZHB9GjRWENDInWEgoqI1CtuTvaM7x7M+O7BxB/LZf7WRKJiEkk4foavtyTy9ZZEmjdxYUxEELdGBBLcxMXskkXkIhRURKTeat7UhUcGtePvN7Rl85HjRMUksnhHCvHHc/n3qn38e9U+erVswtjIIEZ08cfVSb8SRWob/a0UkXrParXQq1VTerVqyrSbO7F8dyrzohNZf/AYGw8fZ+Ph4/xj0W6Gd/FjbEQQ17RqitWqoSGR2kBBRUQaFBdHe27pFsQt3YJIOnmGhVuTmBedyOHM0+dmECUR6NWIWyMCGRMRRAtvV7NLFmnQFFREpMEK9GrEgwPa8ED/1sTEn2RedCLf70gm6eQZ/vPjAf7z4wG6hzRmTGQQN4b54+HsYHbJIg2OgoqINHgWi4XIkMZEhjRm6siOrIxNY150Ij/tz2DL0RNsOXqCad/uZmgnP8ZEBnFdG2/sNDQkclUoqIiI/Iazgx0jwwMYGR5AWvbZkqGh/emn+HZ7Mt9uT8bXw4lbugUxNjKQNj7uZpcsUq8pqIiIXICvhzN/6dea+/u2YmdSFlHRiSzankxadh7/XXuQ/649SHiQJ2MjgxgZHoCXi6PZJYvUOwoqIiKXYLFYCAvyIizIi8k3hrJ6TzrzohNZvTeD7YlZbE/M4qXv4xjU0YcxEUH0bdcMBzur2WWL1AsKKiIiVeBkb8ewzv4M6+xP5qk8Fm1LZl50InEp2SzZmcqSnal4uzkyumsgYyKDCPX3MLtkkTpNQUVE5DJ5uzlx33Utue+6luxOziIqOolF25LIPJXPhz8f5sOfD9MpwIMxEUGM6hpAUzcns0sWqXMUVEREqkGnAE86BXjy7IgOrN2bwbzoRH7Yk8bu5Gx2J8cyfUkcAzrYhoZu6OCDo72GhkQqQ0FFRKQaOdhZGdTRl0EdfTlxOp/vdtiGhnYkZrEyNo2VsWk0dnFgVFfbDeU6B3roAYkiF6GgIiJSQxq7OjKxdwsm9m7BvrQcoqITWbA1ifScPOasP8Kc9Udo7+vOmMhARncNxMfD2eySRWodnXsUEbkK2vm68+yIUNY/cwNz7unBTWH+ONpb2ZuWw/Qle7hmxg/cM3sT3+9I5mxBkdnlitQaOqMiInIV2dtZ6d/eh/7tfcg6U8DiHSnMi04gJv4kq/dmsHpvBh7O9owMD2BMZBDdgr00NCQNmoKKiIhJPBs5MKFXcyb0as6hjFPnHoqYSHLWWT7fGM/nG+Np1cyVMRFB3BoRiL9no8pt2DAgPx+cNMtI6r5aM/QzY8YMLBYLjzzyiNmliIhcda2aufHE0Pb8/PQNfP6nXtzSLRBnByuHMk7zz+V76fPqj9z50UYWbk3iTP4FhoYMA5Yvh169ICQEEhKu7ocQqQG14ozK5s2b+eCDDwgLCzO7FBERU1mtFq5t4821bbx5aXRnluxMYV50IpsOH+en/Zn8tD8TNyd7buziz5jIIHq0aAyGQbOtW7F76SWIjgarFYqLISMDgoPN/kgiV8T0oHLq1CnuuOMO/u///o+XX37Z7HJERGoNNyd7xncPZnz3YOKP5RIVk8j8rYkkHD/D3C0JzN0cz9hjsTzx06f02bcLw87O9sbiYnMLF6lGpgeVBx98kBtvvJFBgwZdMqjk5eWRl5dX8jo7OxuAgoICCgoKqrWu89ur7u3WR+qrylNfVZ76qix/Dwce6t+SB/q2YEv8CXZ+soBrP/4XXVL2U2ixjeJbisoOCRUUFoL6rwwdV1VTU/1Vle2ZGlS++uorYmJi2Lx5c6XWnzFjBi+88EK59hUrVuDi4lLd5QGwcuXKGtlufaS+qjz1VeWpryo24ZNX8EhJBMDeqPgMyhfLfsEjOQWrJg2Vo+Oqaqq7v3Jzcyu9rmlBJSEhgUmTJrFixQqcnSt3k6Nnn32Wxx57rOR1dnY2wcHBDBkyBA+P6n3wV0FBAStXrmTw4ME4ODhU67brG/VV5amvKk99dXGW//s/ip97Dmt0NIadXbmzKQBfH7JywsGN0V0DuLVbACFNa+YfdHWJjquqqan+Oj8iUhmmBZXo6GjS09OJjIwsaSsqKmLdunW8++675OXlYXd+vPUcJycnnCqYbufg4FBjB1xNbru+UV9Vnvqq8tRXFzBsGAwdCitWYEyZgqWCwOLqZMfurLPMXHuImWsP0T2kMWMig7gxzB8P54bdpzquqqa6+6sq2zItqAwcOJCdO3eWabvnnnvo0KEDTz/9dLmQIiIiv2OxwNChFA0YwIbp07nm+++x/GbWz6f39WK5UyBR0Yn8tD+DLUdPsOXoCaZ9u5uhnfwYExnEdW28sdPYkNRipgUVd3d3OnfuXKbN1dWVpk2blmsXEZGLsFjI6NaNosmTsa5eDc8/DwkJOAX4c3NQADeHB5CWfZYFW5OIik5kf/opvt2ezLfbk/H1cOKWbkGMjQykjY+72Z9EpBzTZ/2IiEg1OXeGhSFDyt2Z1tfDmb/2a81f+rZiZ1IW86IT+XZ7MmnZefx37UH+u/Yg4cFejI0IZGR4AF4ujiZ+EJFStSqorFmzxuwSRETqPovlgrfPt1gshAV5ERbkxZQbQ/kxLp2omERW781ge8JJtiec5KXv4xjU0YcxEUH0a9cMe7tacxNzaYBqVVAREZGrx8nejuFd/BnexZ+MnDwWbUsiKiaJuJRsluxMZcnOVLzdnBjd1faAxFD/6p1dKVIZCioiIkIzdyf+dH0r/nR9K3YnZxEVncSibUlknsrjw58P8+HPh+kU4MGYiCBGdQ2gqZseeChXh4KKiIiU0SnAk04Bnjw7ogNr9mYQFZ3ID3vS2J2cze7kWKYviWNAB9vQ0A0dfHC019CQ1BwFFRERqZCDnZXBHX0Z3NGXE6fz+XZ7MlExiexIzGJlbBorY9No7OLAqK6BjI0MolOABxaLpjpL9VJQERGRS2rs6shdfVpwV58W7EvLISo6kQVbk0jPyWPO+iPMWX+E9r7ujIkMZHS3QHzcK3fHcZFLUVAREZEqaefrzrMjQnlyaHt+OpBJVHQiK2LT2JuWw/Qle3ht2V76tvVmbGQwA0N9cHbQDTzl8imoiIjIZbG3szKgvQ8D2vuQlVvA9zuTiYpOJCb+JKv3ZrB6bwYezvaMDLfNGuoW7KWhIakyBRUREblini4O3NErhDt6hXAw4xTzYxKZH5NEStZZPt8Yz+cb42nVzJUxEUHcGhGIv2cjs0uWOkJBRUREqlXrZm48ObQDjw1uz68HjxEVk8jSXSkcyjjNP5fv5Y0Ve7mujTdjIoIY2smPRo4aGpILU1AREZEaYWe1cF1bb65r682LozqxdGcq82IS2XT4OD/tz+Sn/Zm4OdlzYxd/xnYPontIYw0NSTkKKiIiUuPcnR0Y3yOY8T2CiT+WS1RMIvO3JpJw/AxztyQwd0sCIU1duLWbbWgouImL2SVLLaGgIiIiV1Xzpi48Orgdkwa2ZdOR40RFJ7JkZwpHj+Xy71X7+PeqfVzTqgljI4MZ3tkPVyd9VTVk+umLiIgprFYL17RqyjWtmvLCqE4s25VKVEwi6w8eY8Oh42w4dJx/LNrFsM5+jI0M4pqWTbFaNTTU0CioiIiI6Vwc7bk1IohbI4JIOnmGBTGJzItO5MixXObHJDE/JolAr0aMiQjk1oggWni7ml2yXCUKKiIiUqsEejXioRva8uCANsTEn2BedBLfb08m6eQZ3vnxAO/8eIDuIY0ZGxnEiDB/PJwdzC5ZapCCioiI1EoWi4XIkCZEhjRh6siOrIhNY150Ij/vz2DL0RNsOXqCqd/uZmgn29DQtW28sdPQUL2joCIiIrWes4MdN4cHcHN4AGnZZ1mwNYl50YkcSD/Ft9uT+XZ7Mn4eztwSEciYiCDa+LiZXbJUEwUVERGpU3w9nPlrv9b8pW8rdiRmERWTyKJtyaRmn2XWmoPMWnOQ8GAvxkYGMTLMHy8XR7NLliugoCIiInWSxWIhPNiL8GAvptwYyo9x6UTFJLJ6bwbbE06yPeEkL30Xy6COPoyNDKJv22ZmlyyXQUFFRETqPCd7O4Z38Wd4F38ycvJYtM02NLQnNYclO1NZsjMVbzcnbg7zo9lps6uVqlBQERGReqWZuxN/ur4Vf7q+FbuTs4iKTmLRtiQyT+Xx8fqjgD3fZfzKuO7B3BweQFM3J7NLlotQUBERkXqrU4AnnQI8eXZEB9bszeCbLfH8EJdGbEoOL3wXyyuL4xjQwTY0NKC9D472VrNLlt9RUBERkXrPwc7K4I6+9G/bhK8XLSHPtzMLtqWwMymLlbFprIxNo4mrIzeHBzA2MohOAR56QGItoaAiIiINipsDjL+mOfde35p9aTlERScyf2sSGTl5zFl/hDnrj9De152xkUGM6haAj7uz2SU3aAoqIiLSYLXzdefZEaE8ObQ9Px3IZF50Iitj09iblsMrS+J4ddke+rVrxpiIIAaG+uDsYGd2ybVGZm4mH0R/wIqDK9iTuYdjZ45RWFx4wfVX37Wa/i36V3k/CioiItLg2dtZGdDehwHtfcjKLeD7ncnMi05ka/xJftyTzo970vFwtufmrgGMiQiia7BXgx4a+iD6Ax5b/hinC2p+CpWCioiIyG94ujhwR68Q7ugVwsGMU0RFJ7JgaxIpWWf5bEM8n22Ip3UzV8ZEBnFrtyD8PBvW0NDL617m+dXPX3B5gHsAXXy6AHCm8Azrjq67ov0pqIiIiFxA62ZuPDWsA48Pac+vB48xLzqBZbtTOZhxmteX7eWfy/dyXRtvxkYGMaSjH40c6/fQ0OrDq/nH6n9cdJ3BrQYzZ/QcAI6cPELLt1te0T4VVERERC7BzmrhurbeXNfWm5yzBSzdmcq86EQ2HTnOT/sz+Wl/Jm5O9twU5s+YyCC6hzSul0ND/1jzDwyMq7pPBRUREZEqcHd2YHyPYMb3CCb+WC5RMYlExSSSeOIMX21O4KvNCYQ0dWFMRBC3RgQS1NjF7JKrRdqpNH6J/+Wq71dBRURE5DI1b+rCo4PbMWlgWzYdOc686ESW7Ezh6LFc/rVyH/9auY/erZoyJjKI4Z39cHWqu1+729O2X/WzKaCgIiIicsWsVgvXtGrKNa2a8uKoTizbZRsa+vXQsZI//1i0i+Gd/RkTGcg1LZtitdatoaHM3ExT9qugIiIiUo1cHO25NSKIWyOCSDyRy4KYJKJiEjnym2GiQK9GjIkI5NaIIFp4u5pdcqW4OJgzhKWgIiIiUkOCGrvw8MC2PHRDG2LiTzAvOpHvt6eQdPIM7/x4gHd+PECPFo0ZExHEiDB/PJwdzC75glp4tTBlvwoqIiIiNcxisRAZ0oTIkCZMHdmJFbFpzItO5Of9GWw+coLNR04w9dvdDOvsx5iIIK5t441dLRsaCvMNo5lLMzJyM67qfhVUREREriJnBztuDg/g5vAAUrPOsmCrbWjoQPopFm1LZtG2ZPw8nLklIpAxEUG08XEzu2QArBYrD/V8iKlrpl7d/V7VvYmIiEgJP09n/ta/NSsf7cuiB6/lzmtC8GzkQGr2WWatOcigf61l9Hu/8OmGo2TlFphdLk/2eZJuft2u6j4VVERERExmsVgID/bipdGd2TRlIDPviGBgBx/srBa2JZzk+YW76PHKKh78PIYf96RRWFRsSp2NHBqx7I/LuDb42qu2Tw39iIiI1CJO9naM6OLPiC7+ZOTksWhbEvOiE9mTmsPinSks3pmCt5sTt3QLYExkEB38PK5qfT6uPqy9ey3/2/4/3tv8HtEp0TW6PwUVERGRWqqZuxN/ur4Vf7q+FbuTs5gXnciibclknsrj/346zP/9dJjOgR6MiQhiVNdAmrg6XpW67Kx23NPtHu7pdg+pp1LZlb6Lvy/9O3GZcdW+LwUVERGROqBTgCedAjyZPCKUNXszmBedwI970tmVlM2upFheWRzHDR18GBMZxID2PjjaX52rO/zc/PBz88PH1UdBRUREpKFzsLMyuKMvgzv6cvx0Pt9uSyIqJomdSVmsiE1jRWwaTVwduTk8gLGRQXQK8KjTD0hUUBEREamjmrg6cve1Lbn72pbsTc0hKiaRBVuTyMjJY876I8xZf4QOfu62oaFuAfi4O5tdcpVp1o+IiEg90N7PnckjQvn1mRuYfXcPbgzzx9Heyp7UHF5ZEkfvGT9y75zNLN6RwtmCIrPLrTSdUREREalH7O2sDOjgw4AOPmTlFvDdjmSiYhLZGn+SH/ek8+OedDwbOTAy3J+xkcGEB3lWODRUVFzE2qNrWXdiHa5HXRnQagBWrOSfysfJw+mqfR5Tz6jMmjWLsLAwPDw88PDwoHfv3ixdutTMkkREROoNTxcH/nhNCAseuJYfHu/HA/1b4+/pTNaZAj7bEM/o935h0L/WMnPNAVKzzpa8b37cfFq83YLBnw/mX0f/xeDPB+P3UgBtI94mpHEWCRuTr9pnMPWMSlBQEK+++ipt2rQB4JNPPmHUqFFs3bqVTp06mVmaiIhIvdK6mRtPDevA40Pas/5gJlHRiSzbncrBjNO8vmwvbyzfy7VtvAn038Hrm/+CgVHm/ZlGBpmjH4P85mQcCCW4V8BVqbvKQeXuu+/m3nvvpW/fvle885EjR5Z5/corrzBr1iw2bNigoCIiIlID7KwWrm/bjOvbNiPnbAFLdqYQFZ3EpiPHWbc/jaT4yRgWA34/GmQxwLDAsEcoMpZctXqrHFRycnIYMmQIwcHB3HPPPdx1110EBgZecSFFRUV88803nD59mt69e1e4Tl5eHnl5eSWvs7OzASgoKKCgoHqfgXB+e9W93fpIfVV56qvKU19Vnvqq8tRXZTnbwa1d/bm1qz9Hj+fy5tqF/Dcu88JvsBjgmcCW05vpWtC+zCLDsJ2BKS4urrCfCwsLL6v/Lcb5LVfBsWPH+Oyzz5gzZw67du1i0KBB3HfffYwaNQoHB4cqbWvnzp307t2bs2fP4ubmxhdffMGIESMqXHfatGm88MIL5dq/+OILXFxcqvoxREREBLAYRfhk7yQ6dR4Pndl1yfXvy32AkX2GlGmbsn8Ku0/vZkDjAUwKmQRAWl4af4n7CwAvtX6JLu5dAMjNzWXChAlkZWXh4XHxRwBcVlD5ra1bt/Lxxx/z4Ycf4ubmxh//+EceeOAB2rZtW6n35+fnEx8fz8mTJ4mKiuLDDz9k7dq1dOzYsdy6FZ1RCQ4OJjMz85IftKoKCgpYuXIlgwcPrnL4amjUV5Wnvqo89VXlqa8qT331O+mxWHd8hXXXPCyn01lDIQMsuZd820y/j/nTvX8s0zbos0Gsi1/HnV3u5KORHwFw5OQR2s1sB8DKO1bSL6QfYPv+9vb2rlRQuaKLaVNSUlixYgUrVqzAzs6OESNGsHv3bjp27Mjrr7/Oo48+esltODo6llxM2717dzZv3szbb7/N+++/X25dJycnnJzKT4lycHCosQOuJrdd36ivKk99VXnqq8pTX1Veg+6r08dg5zew/QtI2V7a7tKU6zuPJSj2fySdTi93MS1gu0YlO4jurXuU67/zU5ytVmvJst+uY29vX2H7pVQ5qBQUFPDtt98ye/ZsVqxYQVhYGI8++ih33HEH7u7uAHz11Vf87W9/q1RQ+T3DMMqcNREREZErVJgPB1bCti9g33IoPneNiNUB2g2FrhOgzWDs7B15u+U1jP16LBYsZcOKce7q2mVvYRdpd9VKr3JQ8ff3p7i4mNtvv51NmzbRtWvXcusMHToULy+vS25r8uTJDB8+nODgYHJycvjqq69Ys2YNy5Ytq2pZIiIi8luGAak7bOFk5zeQe6x0mX9XWzjpPBZcm5Z5262htzJv/DwmLZtEYnZiSXsziw8eC57h9N7r8Gl39e5sW+Wg8u9//5tx48bh7Hzh5wU0btyYw4cPX3JbaWlp3HnnnaSkpODp6UlYWBjLli1j8ODBVS1LREREAE6lw46vbQElfXdpu6sPhN8G4RPAt/x1oL91a+itjGo/itWHVrP056UMv2647c60z1/4zrQzb5xJdl42zVyalbT5u/nz632/AtCx2cX3eSFVDip33nnnZe2oIh999FG1bUtERKTBKsyDvUtt4eTAKjDOnfGwc4QON9rCSesbwK7yX/t2Vjv6hfTj9O7T9Avph53VNtxzodvnVxREnOyduCbomqp/nt/Qs35ERETqIsOApBjY9jnsioKzJ0uXBfWA8Nuh863QqLFpJVYHBRUREZG6JDsZtn8F27+EzH2l7R6BEHab7doT78rdIqQuUFARERGp7QrOwJ7FtrMnh9aAUWxrt28EoSOh6+3Qsh9Yr95snKtFQUVERKQ2MgxI2GgLJ7sXQl526bLmfWzhpONocK7eG57WNgoqIiIitcnJ+NKhneOHSts9m9vCSfgfoEkr8+q7yhRUREREzJZ3CuK+s509OfJTabuDK3QabbswNuRasFpNK9EsCioiIiJmKC6Go7/YphTHLoKC06XLWva1TSkOHQlObubVWAsoqIiIiFxNxw+VDu2cjC9tb9wSut5huymbV3Pz6qtlFFRERERq2tlsiF1oO3sS/2tpu5MHdLrFNqU4uBece7CflFJQERERqQnFRXB4LWz70nb9SeGZcwss0HqA7exJhxvBoZGpZdZ2CioiIiLVKXO/7czJjrmQnVTa7t3OduYk7DbwCDCvvjpGQUVERORKnTkBu+bbAkrSltJ2Zy/oMtZ2YWxghIZ2LoOCioiIyOUoKoSDP9qmFO9dCkV5tnaLHbQdbJtS3H442Ff8ED+pHAUVERGRqkiLhe1fwI6v4VRaabtPJ9vQTpdx4O5rXn31jIKKiIjIpZw+Brvm2c6epGwvbXdpCl3G2+4Y6xemoZ0aoKAiIiJSkaIC2L/Cdt3JvuVQXGBrt9pDu2G2sydtBoO9o7l11nMKKiIiIucZBqTusE0p3vk15B4rXeYfbptS3HksuDY1r8YGRkFFRETkVLrtmpPtX0LartJ2Vx8IG287e+Lbybz6GjAFFRERaZgK82yzdbZ/CftXglFka7dzhPYjbGdPWt8AdvqqNJN6X0REGg7DwOv0QazLnoLd8+HsydJlgd1tF8V2uhVcmphWopSloCIiIvVfdjLsmIv9ti/ol7mvtN09wPYQwPAJ0KydefXJBSmoiIhI/VRwBvYsts3aObQajGIsQKHFEWvHkVgj/ggt+4HVzuxK5SIUVEREpP4wDEjYaAsnuxdAXnbpsua9KexyG8sTGjFk5BisDg7m1SmVpqAiIiJ138l42D7XdsfY44dK2z2b2647Cf8DNGmFUVBAYfIS8+qUKlNQERGRuin/NMR+awsnh9eVtju4QsdRtinFIdeC1WpejXLFFFRERKTuKC6Go7/YphTvXggFp0uXtbjeNqU4dCQ4uZlWolQvBRUREan9jh+C7V/ZAsrJ+NL2xi1tZ07CboPGIebVJzVGQUVERGqns9kQu9B2O/v49aXtTh7QabTt7ElwLz0IsJ5TUBERkdqjuAgOr7WFk7jvoPDMuQUWaD3Adr+TDjeCo4upZcrVo6AiIiLmy9xvm1K8Yy5kJ5W2e7eD8NttQzuegebVJ6ZRUBEREXOcOQG75tuuO0ncXNru7Gl7QnHXCRAYqaGdBk5BRURErp6iQjj4o21K8Z4lUJRna7fYQZtBtnuetBsODs7m1im1hoKKiIjUvLRYWzjZ8TWcSitt9+lkCyddxoO7r3n1Sa2loCIiIjXj9DHYNc927UnKttJ2l6bQZZxtaMcvTEM7clEKKiIiUn2KCmD/Cls42bccigts7VZ7aDfMdmFs2yFg72hunVJnKKiIiMiVS9lhCyc7v4HczNJ2/3DblOIuY8HV27z6pM5SUBERkctzKt12zcn2LyFtV2m7qw+EjbcN7fh2Mq8+qRcUVEREpPIK82DvUls42b8SjCJbu50jtB9hCyetB4Kdvl6keuhIEhGRizMMSI45N7QzD86eLF0W2N02a6fTreDSxLQSpf5SUBERkYplJ9vuFLvtS8jcW9ruHgDht9muPWnWzrz6pEFQUBERkVIFZ2DPYtvZk0OrwSi2tds7Q+hI26ydVv3BamdqmdJwKKiIiDR0hgEJm2Db57B7IeRllS5r3tsWTjqNtt3aXuQqU1AREWmoTibA9q9sF8YeP1ja7tkcwv9g+9O0tXn1iaCgIiLSsOSfhthvbbezP/wTYNjaHVyh4yjbhbEh14HVamqZIucpqIiI1DOGAfn54OR0rqG4GOLX2647iV0E+adKV25xvW1KcejN4ORmSr0iF2NqUJkxYwbz589nz549NGrUiD59+vDaa6/Rvn17M8sSEamTDAOWL4fnn4f4eNi88ijBmZ/bhnZOxpeu2LilLZyE3QaNQ8wrWKQSTA0qa9eu5cEHH6RHjx4UFhYyZcoUhgwZQmxsLK6urmaWJiJSZxgGbN3ajJdesiM6GqwWg2LDQsa7dxLsv922kqM7dL7FNqW4+TV6EKDUGaYGlWXLlpV5PXv2bHx8fIiOjqZv374mVSUiUjcYBqxYAVOm2BEd3Qc7q+0uscXG+RBigdY32MJJhxvB0cW8YkUuU626RiUryzYlrkmTiu9umJeXR15eXsnr7OxsAAoKCigoKKjWWs5vr7q3Wx+prypPfVV56quL++EHC889U0D09kbYWYoBK0XFZe9tUnjbVxRc/5sHAaovdVxVUU31V1W2ZzEMw6jWvV8mwzAYNWoUJ06c4KeffqpwnWnTpvHCCy+Ua//iiy9wcdG/FESk/rMvPE3gyY3cNnkS+9JbXXTdN99cQ+vWWRddR8QMubm5TJgwgaysLDw8PC66bq0JKg8++CCLFy/m559/JigoqMJ1KjqjEhwcTGZm5iU/aFUVFBSwcuVKBg8ejIODQ7Vuu75RX1We+qry1Fe/UVyI5dAarDu/wrJ3KZaiPFYd6s+zP0xlS3IEdtZiiorLTyfeuLGAbt1MqLcW03FVNTXVX9nZ2Xh7e1cqqNSKoZ+HH36Yb7/9lnXr1l0wpAA4OTnhVDLfrpSDg0ONHXA1ue36Rn1VeeqrymvQfZUWa7vfyY6v4VRaabtPRwYNGcTAdwNZ8StMmQLR0WBnZ1BUVHqRrL29Aw216y6lQR9Xl6G6+6sq2zI1qBiGwcMPP8yCBQtYs2YNLVu2NLMcERHz5R63PaF42+eQsq20vVETCBtvu529fzhYLFiAoUNhwIAipk/fwPffX0N0tAWr1XbrFJH6wNSg8uCDD/LFF1+waNEi3N3dSU1NBcDT05NGjRqZWZqIyNVTVAD7V9rCyb7lUHzuQkOrPbQbZgsnbYeAvWOFb7dYoFu3DCZPLmL1aivPPw8JCeDjcxU/g0gNMTWozJo1C4D+/fuXaZ89ezZ333331S9IRORqStlhu1vszm8gN7O03T/cNqW4y1hw9b7w+3/HYrGdYRky5Hd3phWpw0wf+hERaVBOpduCybYvIG1Xaburj21op+sE8O10RbuwWBRSpP6oFRfTiojUa4V5sG+ZLZzsXwmG7cZs2DlC+xG2cNJ6INjpV7LI7+lvhYhITTAMSI6BbV/Crnlw5kTpssBIWzjpdCu4VHyDSxGxUVAREalO2SmwY67t7Enm3tJ2d38I/4PtwthmevCqSGUpqIiIXKmCM7Bnse0pxQd/BOPc3GB7Z+hwk+3sSav+YLW76GZEpDwFFRGRy2EYkLDJdkO2XQsg7ze3qg++5tzQzmhw9jStRJH6QEFFRKQqTibAjq9s154cP1ja7hlsG9YJ/wM0bW1efSL1jIKKiMil5J+GuO9sN2Q7/BNw7tYKDq7QcRR0vR1CrgNr+eftiMiVUVAREalIcTHEr7edOYldCPmnSpe1uN42tBN6Mzi5mVaiSEOgoCIi8lvHD8P2r2zXnpyML21v3AK63gFht0HjENPKE2loFFRERPJyYPdC26ydo7+Utju62y6I7XoHNL/GdstXEbmqFFREpGEqLoLD62zhJPZbKDxzboHFNpW46x3Q4UZwdDGzSpEGT0FFRBqWzAO2YZ3tcyE7sbS9aVvbRbFhfwDPQPPqE5EyFFREpP47cxJ2z7ddGJu4qbTd2RM6j7GdPQmM1NCOSC2koCIi9VNRIRxabbuV/Z7FUJRna7dYoc0g2z1P2o8AB2dz6xSRi1JQEZH6JT3OFk52fA2nUkvbfTrawknYeHD3M68+EakSBRURqftyj8POebYbsqVsK21v1AS6jLPd88Q/XEM7InWQgoqI1E1FBbB/pe3C2L3LoLjA1m61h7ZDbeGk7RCwdzS3ThG5IgoqIlK3pOywTSne8TXkZpa2+4XZLortMhZcvc2rT0SqlYKKiNR+pzJg59e2WTtpO0vbXX1s15yE3w5+nc2rT0RqjIKKiNROhXn4n9yM3defw4FVYBTZ2u0cof1w29mT1gPBTr/GROoz/Q0XkdrDMCA5BrZ9if2uefQ8c6J0WWCk7cxJ5zHg0sS8GkXkqlJQERHzZafAjrm2a08y9gBgAc44NMax+53YRfwRmrU3t0YRMYWCioiYo+CM7UZs27+Egz+CUWxrt3eGDjdR2Hk8K/bkMuKGm7BzcDC3VhExjYKKiFw9hgEJm2xTinctgLys0mXB19ietdPpFnD2xCgogL1LzKtVRGoFBRURqXknE2DHV7ZZO8cPlrZ7BkP4H2zXnjRtbV59IlJrKaiISM3IPw1x39luZ394HWDY2h1coOMo2w3ZQq4Dq9XUMkWkdlNQEZHqU1wM8ettZ05iF0L+qdJlLa63nTnpeDM4uZtWoojULQoqInLljh+G7V/ZLow9ebS0vXELCJ9gG95pHGJaeSJSdymoiMjlycuB3Qtt4eToL6Xtju7QabRtaKd5bz0IUESuiIKKiFRecTEcXmsLJ3HfQUHuuQUWaNXfFk463ASOLmZWKSL1iIKKiFxa5gHblOLtcyE7sbS9aVvblOKw28AzyLz6RKTeUlARkYqdOQm759sujE3cVNru7Gm7jX34BAjqrqEdEalRCioiUqq4CA6uhm2f2+4aW5Rna7dYoc0g26yd9iPAwdncOkWkwVBQERFIj7Pd72TH13AqtbTdp6MtnISNB3c/8+oTkQZLQUWkoco9Djvn2a49Sd5a2t6oCXQZZ7sw1j9cQzsiYioFFZGGpKgA9q+0hZO9y6C4wNZutYe2Q20XxrYdCvaO5tYpInKOgopIQ5C6s3RoJzeztN0vzHbmpMs4cPU2rz4RkQtQUBGpr05lwM6vbbN20naWtrs2s00nDr8d/DqbV5+ISCUoqIjUJ4V5sG+57ezJgZVQXGhrt3OE9sNtU4rbDAQ7B3PrFBGpJAUVkbrOMGwXw277AnbNgzMnSpcFRtrOnHQeAy5NzKtRROQyKaiI1FU5qbBjri2gZOwpbXf3tw3tdJ0AzdqbV5+ISDVQUBGpSwrOwt7FtnBy8Ecwim3t9s62Z+x0vR1aDQCrnbl1iohUEwUVkdrOMCBxs+1usbsWQF5W6bLga2zhpNMttlvbi4jUMwoqIrXVyQTY8ZVt1s7xg6XtnsEQ/gfbtSdNW5tXn4jIVaCgImIiw4D8fHByOteQfxrivredPTm8DjBs7Q4u0HGULZy0uB6sVrNKFhG5qkz9bbdu3TpGjhxJQEAAFouFhQsXmlmOyFVjGLB8OfTqBSEhBgnrN8PCB+GNdrDgfji8FjBsoWTUTHhiH9zyX2jVTyFFRBoUU8+onD59mvDwcO655x7GjBljZikiV4VhwNatzXjpJTuio8FqKabYsJLxyeME+2+3rdS4he1+J+G32f5fRKQBMzWoDB8+nOHDh5tZgshVYRiwYgVMmWwhOqYPdpYiAIqNc2dH7F2g2522KcXNe+tBgCIi59Spa1Ty8vLIy8sreZ2dnQ1AQUEBBQUF1bqv89ur7u3WR+qri/thlcHzT59ly04P7M7ljyKj7PThwgnfUNDT+dyLwqtcYe2k46ry1FeVp76qmprqr6psz2IYhlGte79MFouFBQsWMHr06AuuM23aNF544YVy7V988QUuLi41WJ1I1bmeTSX4+M+MmvoP9ma0vei6b765htatsy66johIfZGbm8uECRPIysrCw8PjouvWqaBS0RmV4OBgMjMzL/lBq6qgoICVK1cyePBgHBz0XJSLUV/9xtksLLELse74CmvSZgBWHerPsz++wJakrthZDYqKyw/rbNxYQLduV7vY2k3HVeWprypPfVU1NdVf2dnZeHt7Vyqo1KmhHycnJ5xK5nGWcnBwqLEDria3Xd802L4qLoKDq2H7F7apxUXnwrTFCq0HMmjsBAZ+2IEVq2HKFIPoaAt2dgZFRaWBxd7egYbYdZXRYI+ry6C+qjz1VdVUd39VZVt1KqiI1Crpe2zhZPtcOJVa2t4s1HZRbNh4cPcDwAIMHQoDBhQxffoGvv/+GqKjLVitUFxsTvkiInWBqUHl1KlTHDhwoOT14cOH2bZtG02aNKF58+YmViZyAbnHYVeU7YZsyVtL2xs1gS7jbLez9+96wVk7Fgt065bB5MlFrF5t5fnnISEBfHyuTvkiInWNqUFly5YtDBgwoOT1Y489BsBdd93FnDlzTKpK5HeKCuDAKls42bsMis9drW61h7ZDbeGk7VCwd6z0Ji0W2xmWIUN+d2daEREpw9Sg0r9/f2rJtbwi5aXutD1nZ+fXcDqjtN2vC3S9AzqPBbdmV7QLi0UhRUTkYnSNishvncqAnd/Ati8gbWdpu2szCLvN9qwdv87m1Sci0sAoqIgU5sO+ZbD9S9i/AorP3XDNzhHaDbOdPWkzEOw0Q0BE5GpTUJGGyTBsF8Nu/9J2BuXMidJlARG2WTudx4BLE/NqFBERBRVpYHJSYcdc27UnGXGl7e7+tunE4RPAp4N59YmISBkKKlL/FZyFvYtt4eTgD2Ccu3GJvTN0uNF29qTVALDaXXw7IiJy1SmoSP1kGJC42XZR7O75cPY3z9EJ7mW7KLbTLdDIy7QSRUTk0hRUpH7JSoTtX9muPTlWejNBPIIg/A+2gOLdxrz6RESkShRUpO7LP217xs72L+DQWuDcvXkcXCD0ZtvQTovrwWo1tUwREak6BRWpmwwDjq63hZPdCyH/VOmykOts4aTjzeDkblqJIiJy5RRUpG45ccQ2tLPtCzh5tLS9cQvbjJ3w22z/LyIi9YKCitR+eTkQu8g2a+foz6Xtju7QaZTthmzNe1/wQYAiIlJ3KahI7VRcDEfW2cJJ3LdQkHtugQVa9bOFkw43gaOLqWWKiEjNUlCR2uXYQduwzo65kJVQ2t60jW3GTvgfwDPIvPpEROSqUlAR8505CbsX2KYUJ2wsbXfyhM632s6eBHXX0I6ISAOkoCLmKC6Cg6tts3b2LIbCs7Z2ixVaD4Sut0P7G8HB2dw6RUTEVAoqcnWl77GFkx1fQ05KaXuzUFs46TIePPzNq09ERGoVBRWpebnHYVeU7dqT5JjS9kaNocs427UnAd00tCMiIuUoqEjNKCqAA6ts4WTfMijKt7Vb7aHtEFs4aTcU7J3MrVNERGo1BRWpXqk7bVOKd34NpzNK2/262G7I1mUcuDUzrz4REalTFFTkyp3OoFX6Muw//Cek7Sxtd21mu+ak6+22oCIiIlJFCipyeQrzbUM627/Efv8KuhQX2trtHKHdMNuzdtoMAjsHc+sUEZE6TUFFKs8wIGWb7bqTnfPgzHEALMAJl1Z4XP8X7MLHg0sTU8sUEZH6Q0FFLi0n1Xan2G1fQkZcabubH4TfRkGn8azbfJAR3Udg56AzKCIiUn0UVKRiBWdh72JbODn4AxjFtnY7Jwi9yXZhbKv+YGcPBQXAQTOrFRGRekpBRUoZBiRugW2fw+75cDardFlwL9uU4k63QCMv00oUEZGGRUFFICsRtn9le9bOsQOl7R5BtocAht8O3m3Mq09ERBosBZWGKj8X9nxvO3tyaC1g2NodXCD0ZtuU4hZ9wWo1tUwREWnYFFQaEsOAo+ttz9rZvQjyc0qXhVxnCycdR4GTu3k1ioiI/IaCSkNw4kjp0M6JI6XtXiG2+52E/wEatzCpOBERkQtTUKmv8nIgdpFt1s7Rn0vbHd2g02jbrJ3mvTW0IyIitZqCSn1SXAxHfrLdkC3uWyjIPbfAAq362cJJ6E3g6GpqmSIiIpWloFIfHDtoCyc75kJWQml70za2GTvhfwDPIPPqExERuUwKKnXV2SzYvcAWUBI2lrY7eULnW23XngT1AIvFvBpFRESukIJKXVJcBIdW28LJnsVQeNbWbrFC64G2WTvtR4BDI3PrFBERqSYKKnVBxt7SoZ2clNL2Zh1sZ066jAcPf/PqExERqSEKKrVV7nHYFWULKMkxpe2NGkOXcbZrTwK6aWhHRETqNQWV2qSoAA78YLsh296lUJRva7fYQdshtrMn7YaCvZO5dYqIiFwlCiq1Qeou25mTnV/D6YzSdt8u54Z2xoFbM/PqExERMYmCillOZ8LOb2zP2kndWdru4g1ht9kujPXrYl59IiIitYCCytVUmA/7l9vOnuxfAcWFtnarA7Qfbjt70mYQ2DmYW6eIiEgtoaBS0wwDUradG9qZB2eOly4L6AZd74DOY8CliWklioiI1FYKKjUlJxV2fG0LKBlxpe1ufhB+m+129j4dzKtPRESkDlBQqU4FZ2HvEls4OfgDGMW2djsn2zN2widAq/5gp24XERGpDH1jXinDgMQttinFu6Jst7Y/L6in7bqTTrdAIy/TShQREamrFFQqqbgYTp0CD49zDVlJsOMr2PYlHNtfuqJHkO0hgOG3g3cbU2oVERGpL6xmFzBz5kxatmyJs7MzkZGR/PTTT2aXVEZxMbzyCri7Q2Mvg42frYT/jYZ/d4IfXrSFFPtGtinFExfBIzth4PMKKSIiItXA1DMqc+fO5ZFHHmHmzJlce+21vP/++wwfPpzY2FiaN29uZmkUF8M337RlwgR7cnMBDMDCgQVz6dVltW2lkGttQzsdR4GTu4nVioiI1E+mnlH517/+xX333cef/vQnQkNDeeuttwgODmbWrFmm1XT+DEqTxnZ8/nnHcyEF4NwzdRp5Q79n4O/b4J4l0O2PCikiIiI1xLQzKvn5+URHR/PMM8+UaR8yZAjr16+v8D15eXnk5eWVvM7OzgagoKCAgoKCK67pjTesvPyyldxcCyXBhLIP/Ssa/BIF1517UQ37rA/O9311/AzqO/VV5amvKk99VXnqq6qpqf6qyvZMCyqZmZkUFRXh6+tbpt3X15fU1NQK3zNjxgxeeOGFcu0rVqzAxcXlimv6xz9uorCw4oBy3rbt2/H0SrrifdVHK1euNLuEOkN9VXnqq8pTX1We+qpqqru/ckuHKy7J9Fk/FkvZQGAYRrm285599lkee+yxktfZ2dkEBwczZMgQPEqm41y+F1+El182zp1RsV2T8ntdu4YzYkT4Fe+rPikoKGDlypUMHjwYBwfd/v9i1FeVp76qPPVV5amvqqam+uv8iEhlmBZUvL29sbOzK3f2JD09vdxZlvOcnJxwcnIq1+7g4FAtHfjss/D00zBjBkyfTpmLaM+zs3NAx3bFquvn0BCorypPfVV56qvKU19VTXX3V1W2ZdrFtI6OjkRGRpY7nbRy5Ur69OljUlVgtcKUKXD8eCF33BFLNYwoiYiIyGUyddbPY489xocffsjHH39MXFwcjz76KPHx8fz1r381syzAFljGjdvP8eOFvPwyuLjY2tq1M7syERGRhsPUa1Ruu+02jh07xosvvkhKSgqdO3dmyZIlhISEmFlWGefPsDz77O/uTCsiIiI1zvSLaR944AEeeOABs8u4JKtVIUVERORqM/0W+iIiIiIXoqAiIiIitZaCioiIiNRaCioiIiJSaymoiIiISK2loCIiIiK1loKKiIiI1FoKKiIiIlJrKaiIiIhIrWX6nWmvhGEYQNUeF11ZBQUF5Obmkp2drSdsXoL6qvLUV5Wnvqo89VXlqa+qpqb66/z39vnv8Yup00ElJycHgODgYJMrERERkarKycnB09PzoutYjMrEmVqquLiY5ORk3N3dsVgs1brt7OxsgoODSUhIwEMP+bko9VXlqa8qT31VeeqrylNfVU1N9ZdhGOTk5BAQEIDVevGrUOr0GRWr1UpQUFCN7sPDw0MHcyWprypPfVV56qvKU19Vnvqqamqivy51JuU8XUwrIiIitZaCioiIiNRaCioX4OTkxNSpU3FycjK7lFpPfVV56qvKU19Vnvqq8tRXVVMb+qtOX0wrIiIi9ZvOqIiIiEitpaAiIiIitZaCioiIiNRaCioiIiJSazXooDJz5kxatmyJs7MzkZGR/PTTTxddf+3atURGRuLs7EyrVq3473//e5UqNV9V+mrNmjVYLJZyf/bs2XMVKzbHunXrGDlyJAEBAVgsFhYuXHjJ9zTU46qqfdVQj6sZM2bQo0cP3N3d8fHxYfTo0ezdu/eS72uIx9Xl9FVDPa4AZs2aRVhYWMnN3Hr37s3SpUsv+h4zjqsGG1Tmzp3LI488wpQpU9i6dSvXX389w4cPJz4+vsL1Dx8+zIgRI7j++uvZunUrkydP5u9//ztRUVFXufKrr6p9dd7evXtJSUkp+dO2bdurVLF5Tp8+TXh4OO+++26l1m/Ix1VV++q8hnZcrV27lgcffJANGzawcuVKCgsLGTJkCKdPn77gexrqcXU5fXVeQzuuAIKCgnj11VfZsmULW7Zs4YYbbmDUqFHs3r27wvVNO66MBqpnz57GX//61zJtHTp0MJ555pkK13/qqaeMDh06lGn7y1/+YlxzzTU1VmNtUdW+Wr16tQEYJ06cuArV1V6AsWDBgouu05CPq9+qTF/puLJJT083AGPt2rUXXEfHlU1l+krHVVmNGzc2PvzwwwqXmXVcNcgzKvn5+URHRzNkyJAy7UOGDGH9+vUVvufXX38tt/7QoUPZsmULBQUFNVar2S6nr87r1q0b/v7+DBw4kNWrV9dkmXVWQz2urkRDP66ysrIAaNKkyQXX0XFlU5m+Oq+hH1dFRUV89dVXnD59mt69e1e4jlnHVYMMKpmZmRQVFeHr61um3dfXl9TU1Arfk5qaWuH6hYWFZGZm1litZrucvvL39+eDDz4gKiqK+fPn0759ewYOHMi6deuuRsl1SkM9ri6HjivbE2cfe+wxrrvuOjp37nzB9XRcVb6vGvpxtXPnTtzc3HBycuKvf/0rCxYsoGPHjhWua9ZxVaefnnylLBZLmdeGYZRru9T6FbXXR1Xpq/bt29O+ffuS17179yYhIYE33niDvn371middVFDPq6qQscVPPTQQ+zYsYOff/75kus29OOqsn3V0I+r9u3bs23bNk6ePElUVBR33XUXa9euvWBYMeO4apBnVLy9vbGzsyt3RiA9Pb1cWjzPz8+vwvXt7e1p2rRpjdVqtsvpq4pcc8017N+/v7rLq/Ma6nFVXRrScfXwww/z7bffsnr1aoKCgi66bkM/rqrSVxVpSMeVo6Mjbdq0oXv37syYMYPw8HDefvvtCtc167hqkEHF0dGRyMhIVq5cWaZ95cqV9OnTp8L39O7du9z6K1asoHv37jg4ONRYrWa7nL6qyNatW/H396/u8uq8hnpcVZeGcFwZhsFDDz3E/Pnz+fHHH2nZsuUl39NQj6vL6auKNITj6kIMwyAvL6/CZaYdVzV6qW4t9tVXXxkODg7GRx99ZMTGxhqPPPKI4erqahw5csQwDMN45plnjDvvvLNk/UOHDhkuLi7Go48+asTGxhofffSR4eDgYMybN8+sj3DVVLWv/v3vfxsLFiww9u3bZ+zatct45plnDMCIiooy6yNcNTk5OcbWrVuNrVu3GoDxr3/9y9i6datx9OhRwzB0XP1WVfuqoR5Xf/vb3wxPT09jzZo1RkpKSsmf3NzcknV0XNlcTl811OPKMAzj2WefNdatW2ccPnzY2LFjhzF58mTDarUaK1asMAyj9hxXDTaoGIZhvPfee0ZISIjh6OhoRERElJnCdtdddxn9+vUrs/6aNWuMbt26GY6OjkaLFi2MWbNmXeWKzVOVvnrttdeM1q1bG87Ozkbjxo2N6667zli8eLEJVV9956c6/v7PXXfdZRiGjqvfqmpfNdTjqqI+AozZs2eXrKPjyuZy+qqhHleGYRj33ntvye/1Zs2aGQMHDiwJKYZRe44ri2GcuxJGREREpJZpkNeoiIiISN2goCIiIiK1loKKiIiI1FoKKiIiIlJrKaiIiIhIraWgIiIiIrWWgoqIiIjUWgoqIiIiUmspqIiIiEitpaAiIiIitZaCioiIiNRaCioiUmtkZGTg5+fH9OnTS9o2btyIo6MjK1asMLEyETGLHkooIrXKkiVLGD16NOvXr6dDhw5069aNG2+8kbfeesvs0kTEBAoqIlLrPPjgg6xatYoePXqwfft2Nm/ejLOzs9lliYgJFFREpNY5c+YMnTt3JiEhgS1bthAWFmZ2SSJiEl2jIiK1zqFDh0hOTqa4uJijR4+aXY6ImEhnVESkVsnPz6dnz5507dqVDh068K9//YudO3fi6+trdmkiYgIFFRGpVZ588knmzZvH9u3bcXNzY8CAAbi7u/P999+bXZqImEBDPyJSa6xZs4a33nqLTz/9FA8PD6xWK59++ik///wzs2bNMrs8ETGBzqiIiIhIraUzKiIiIlJrKaiIiIhIraWgIiIiIrWWgoqIiIjUWgoqIiIiUmspqIiIiEitpaAiIiIitZaCioiIiNRaCioiIiJSaymoiIiISK2loCIiIiK11v8DGOApDTCAKnUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = 0; y1 = 6; v1 = [1, -1]\n",
    "x2 = 0; y2 = 0; v2 = [1, 1]\n",
    "calcular_punto_encuentro(x1, y1, v1, x2, y2, v2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo #2 (misma recta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y1 = 1.0 * x1 + 0.0\n",
      "y2 = 1.0 * x2 + 0.0\n",
      "Las rectas son la misma!\n"
     ]
    }
   ],
   "source": [
    "x3 = 0; y3 = 0; v3 = [1, 1]\n",
    "x4 = 0; y4 = 0; v4 = [1, 1]\n",
    "\n",
    "calcular_punto_encuentro(x3, y3, v3, x4, y4, v4)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo #3 (colisión en el punto de partida)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y1 = 1.0 * x1 + 0.0\n",
      "y2 = 2.0 * x2 + 0.0\n",
      "Hay colisión en el punto de origen\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x5 = 0; y5 = 0; v5 = [1, 1]\n",
    "x6 = 0; y6 = 0; v6 = [1, 2]\n",
    "\n",
    "calcular_punto_encuentro(x5, y5, v5, x6, y6, v6)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo #4 (sin colisión)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y1 = 0.5 * x1 + 0.0\n",
      "y2 = -2.0 * x2 + 1.0\n",
      "No hay colisión\n"
     ]
    }
   ],
   "source": [
    "x7 = 0; y7 = 0; v7 = [2, 1]\n",
    "x8 = 0; y8 = 1; v8 = [1, -2]\n",
    "calcular_punto_encuentro(x7, y7, v7, x8, y8, v8)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias\n",
    "\n",
    "Algunos enlaces que pueden ser de utilidad:\n",
    "\n",
    "- [Recta (Wikipedia)](https://es.wikipedia.org/wiki/Recta)\n",
    "- [Geogebra Calculator](https://www.geogebra.org/calculator)\n",
    "- [Marker\n",
    "  Examples](https://matplotlib.org/stable/gallery/lines_bars_and_markers/scatter_star_poly.html)\n",
    "- [Matplotlib Reference](https://matplotlib.org/stable/api/pyplot_summary.html)\n",
    "- [Floor and Ceil](https://www.geeksforgeeks.org/floor-ceil-function-python/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
